Queueing Systems

, Volume 68, Issue 3–4, pp 353–360

Conditional inter-departure times from the M/G/s queue

  • Casper Veeger
  • Yoav Kerner
  • Pascal Etman
  • Ivo Adan


We study the mean and the distribution of the time elapsing between two consecutive departures from the stationary M/G/s queue given the number of customers left behind by the first departure is equal to n. It is conjectured that if the failure rate of the service time distribution is increasing (decreasing), then (i) the limit of the mean conditional inter-departure time as n tends to infinity is less (greater) than the mean service time divided by the number of servers s, and (ii) the conditional inter-departure times are stochastically decreasing (increasing) in n for all ns.


Departure process Failure rate 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Casper Veeger
    • 1
  • Yoav Kerner
    • 2
  • Pascal Etman
    • 1
  • Ivo Adan
    • 1
    • 3
  1. 1.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Industrial Engineering and ManagementBen Gurion University of the NegevBeer ShevaIsrael
  3. 3.Department of Quantitative EconomicsUniversity of AmsterdamAmsterdamThe Netherlands

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